A study commissioned by the National Football League reports that Alzheimer’s disease or similar memory-related diseases appear to have been diagnosed in the league’s former players vastly more often than in the national population — including a rate of 19 times the normal rate for men ages 30 through 49.

The N.F.L. has long denied the existence of reliable data about cognitive decline among its players. These numbers would become the league’s first public affirmation of any connection, though the league pointed to limitations of this study.

The findings could ring loud at the youth and college levels, which often take cues from the N.F.L. on safety policies and whose players emulate the pros. Hundreds of on-field concussions are sustained at every level each week, with many going undiagnosed and untreated.

A detailed summary of the N.F.L. study, which was conducted by the University of Michigan’s Institute for Social Research, was distributed to league officials this month.